Euclidean tensor calculus with applications:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English Romanian |
| Published: |
Bucureşti
Ed. Tehnicǎ
1983
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Rumän. übers. - EST: Tehnici de calcul tensorial euclidian cu aplicatii (engl.) |
| Physical Description: | 303 S. graph. Darst. |
| ISBN: | 0856263303 |
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| 245 | 1 | 0 | |a Euclidean tensor calculus with applications |c I. Beju ; E. Soós ; P. P. Teodorescu |
| 264 | 1 | |a Bucureşti |b Ed. Tehnicǎ |c 1983 | |
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Record in the Search Index
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| adam_text | Contents
Preface to the Romanian edition 9
Preface to the English edition 11
1 Euclidean tensors 13
1.1 The tensor as an orthogonal invariant 13
1.1.1 Definition. Properties 13
1.1.2 Operations with tensors and pseudotensors 20
1.1.3 Structural properties 35
1.2 Tensors of second order 45
1.2.1 General properties 45
1.2.2 Structural properties 49
1.2.3 Eigenvalues and eigenvectors 54
1.2.4 Properties of eigenvectors and eigenvalues 59
1.2.5 Invariants of tensors of second order 67
1.2.6 Additive decompositions of tensors of second order 73
1.3 Tensor fields 74
1.3.1 Differential operators 74
1.3.2 Integral formulae 78
2 Tensors on linear spaces 81
2.1 The tensor as an element of a linear space 81
2.1.1 Dual space 81
2.1.2 Multilinear mappings 87
2.2 Tensors on Euclidean spaces 92
2.2.1 Euclidean and pseudo Euclidean spaces 92
2.2.2 Notions about tensors 95
2.2.3 Tensors on Euclidean spaces 99
3 Applications to geometry 101
3.1 Geometry of curves and surfaces 101
3.1.1 Geometry of curves 101
3.1.2 Geometry of surfaces 104
6 CONTENTS
3.2 Curvilinear co ordinates Ill
3.2.1 Arbitrary curvilinear co ordinates Ill
3.2.2 Orthogonal curvilinear co ordinates 120
4 Applications to mechanics of solids 131
4.1 Mechanics of a rigid solid 131
4.1.1 Equations of equilibrium and motion of a rigid solid 131
4.1.2 The rigid solid with a fixed point 145
4.2 Mechanics of deformable solids 152
4.2.1 Geometry and kinematics of deformation 153
4.2.2 Mechanics of stresses 161
5 Applications to acoustics 175
5.1 Plane progressive waves 175
5.1.1 The acoustic tensor. Properties 175
5.1.2 Plane progressive waves 177
5.2 Free vibrations 180
5.2.1 Fundamental relations 180
5.2.2 Characteristic vibrations 182
6 Applications to crystallography 185
6.1 Generalities 185
6.1.1 Elements of crystallography 185
6.1.2 Geometrical structure of crystals 186
6.2 The totality of possible crystalline classes 187
6.2.1 The concept of crystalline symmetry 187
6.2.2 Derivation of all possible classes of crystal 194
7 Applications to the theory of time and space 199
7.1 The aether 199
7.1.1 Inertial frames of reference 199
7.1.2 Maxwell s electrodynamics 202
7.1.3 Lorentz s electrodynamics 206
7.2 The Einsteinian time 212
7.2.1 The velocity of light in vacuo. The time of an inertial reference
system 212
7.2.2 The Lorentz Poincare Einstein transformation 217
7.3 The four dimensional world of events 224
7.3.1 The Minkowskian space time 224
7.3.2 The properties of the Minkowskian world 229
7.3.3 The four dimensional pseudo Euclidean space—the mathematical model
of the world of events 233
8 Applications to electromagnetism and to optics 243
8.1 Relativistic kinematics 243
8.1.1 Velocity and composition of velocities 243
8.1.2 Applications. Acceleration 246
CONTENTS 7
8.2 The electromagnetic field 247
8.2.1 The relativistic interpretation of Lorentzian theory 247
8.2.2 The ponderomotive action of the electromagnetic field 253
8.3 Electromagnetics and optics of moving media 263
8.3.1 The electromagnetic field in vacuo 263
8.3.2 Dynamic and energy characteristics of the plane wave 270
9 Applications to the relativistic mechanics of a particle 275
9.1 Dynamics of a particle 275
9.1.1 Mechanics and the principles of relativity 275
9.1.2 Planck s dynamics. Rest mass and relativistic mass 281
9.2 Relativistic mechanics of a particle in the four dimensional world of events . . 287
9.2.1 Minkowski s dynamics. The synthesis of conservation laws of momentum
and energy 287
9.2.2 Hyperbolic motion. The linear accelerator 289
Bibliography 291
Author index 295
Subject index 297
|
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| id | DE-604.BV001999555 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:39Z |
| institution | BVB |
| isbn | 0856263303 |
| language | English Romanian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001304324 |
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| owner_facet | DE-91G DE-BY-TUM DE-384 DE-824 DE-11 DE-83 |
| physical | 303 S. graph. Darst. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Ed. Tehnicǎ |
| record_format | marc |
| spelling | Beju, Iulian Verfasser aut Euclidean tensor calculus with applications I. Beju ; E. Soós ; P. P. Teodorescu Bucureşti Ed. Tehnicǎ 1983 303 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus d. Rumän. übers. - EST: Tehnici de calcul tensorial euclidian cu aplicatii (engl.) Calculus of tensors Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Euklidischer Raum (DE-588)4309127-1 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 s Euklidischer Raum (DE-588)4309127-1 s DE-604 Soós, Eugen Verfasser aut Teodorescu, Petre P. 1929- Verfasser (DE-588)133443086 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001304324&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beju, Iulian Soós, Eugen Teodorescu, Petre P. 1929- Euclidean tensor calculus with applications Calculus of tensors Tensorrechnung (DE-588)4192487-3 gnd Euklidischer Raum (DE-588)4309127-1 gnd |
| subject_GND | (DE-588)4192487-3 (DE-588)4309127-1 |
| title | Euclidean tensor calculus with applications |
| title_auth | Euclidean tensor calculus with applications |
| title_exact_search | Euclidean tensor calculus with applications |
| title_full | Euclidean tensor calculus with applications I. Beju ; E. Soós ; P. P. Teodorescu |
| title_fullStr | Euclidean tensor calculus with applications I. Beju ; E. Soós ; P. P. Teodorescu |
| title_full_unstemmed | Euclidean tensor calculus with applications I. Beju ; E. Soós ; P. P. Teodorescu |
| title_short | Euclidean tensor calculus with applications |
| title_sort | euclidean tensor calculus with applications |
| topic | Calculus of tensors Tensorrechnung (DE-588)4192487-3 gnd Euklidischer Raum (DE-588)4309127-1 gnd |
| topic_facet | Calculus of tensors Tensorrechnung Euklidischer Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001304324&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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